# Good method to store pyramid shaped cell array?

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Xiaohan Du on 15 Jan 2018
Edited: Xiaohan Du on 18 Jan 2018
Hi all,
I need to store some matrices in a cell, say I have 4 matrices: e1, e2, e3, e4, I need to compute the product of the matrix transpose and the matrix itself like:
e1' * e1; e1' * e2;
e2' * e2; e2' * e3;
e3' * e3; e3' * e4;
e4' * e4;
So the matrix transpose product itself, and the matrix transpose multiply the next matrix. I can use a 4-by-2 cell to store these, but the last cell element would be void, any better ways? I'd like to keep the hierarchical structure. Cheers!
Edit: I'm sorry, I should have made the question clearer. I just generate a 4-by-2 cell array and store these in it, leaving the last cell element void. I think it is fine for now.

Darshan Ramakant Bhat on 18 Jan 2018
You can make use the of the linear indexing of MATLAB. Basically 2D matrix can be stored as a single dimension cell array. To access a particular row,column you can convert the subscript to linear index and then access it from the array. Example code can be like below:
MAT_cell = cell(1,7);
MAT_cell{1} = "e1'*e1";
MAT_cell{2} = "e2'*e2";
MAT_cell{3} = "e3'*e3";
MAT_cell{4} = "e4'*e4";
MAT_cell{5} = "e1'*e2";
MAT_cell{6} = "e2'*e3";
MAT_cell{7} = "e3'*e4";
matSize = [4 2];
% The index (3,2) can be accessed like below:
linIndex = sub2ind(matSize,3,2);
val = MAT_cell(linIndex)

Walter Roberson on 18 Jan 2018
I do not understand why you used "" string objects in combination with cell arrays? If you were trying to create an array of string objects then use MAT_cell = strings(1,7) and use () indexing instead of {} indexing.
But it looks to me as if the poster is not interested in constructing strings and instead wants actual computation.
Darshan Ramakant Bhat on 18 Jan 2018
Hi Walter,
I just represented matrices as string, just for the understanding and simplicity purpose. The string should be replaced by the actual matrix in the original implementation.

Jos (10584) on 18 Jan 2018
If you have too many void cells in an array, you could consider a sparse encoding scheme, where you store the indices and the contents of your cell structure, similar to SPARSE. In your case however, having a single void cell, I would not take the trouble. Nonetheless, here is one approach:
C = {'one',[],[] ; [] 2 [] ; [] 3 4 ; [] [] [] ; 5 '6' []} % a cell array with many voids
% encode into sparse format using a structure
tf = ~cellfun(@isempty,C) ; % non-empty cells
S.size = size(C) ;
S.index = find(tf) ; % index
S.values = C(tf) ;
whos % encoding into sparse saves some memory ...
% rebuild
C2 = cell(S.size) ;
[C2{S.index}] = deal(S.values{:})
isequal(C, C2) % check ...